Output torque is the most important number on a worm gearbox selection sheet — and the most frequently miscalculated. Engineers routinely overestimate it by forgetting efficiency, misapply service factors, or confuse nominal torque with peak torque. A 15% calculation error at this stage means either a gearbox that fails prematurely under shock load, or one that is one frame size larger than needed and costs 30–40% more. This article gives you the exact worm gearbox torque calculation procedure: the complete formula, every variable defined with typical values, three fully worked examples covering different application types, and a reference table of efficiency values for each ratio so you can calculate without a catalog in front of you.

The Core Output Torque Formula — All Four Variables Defined

The output torque of a worm gearbox is:

Where each variable means:

The most common mistake is omitting η — using T₂ = T₁ × i without the efficiency factor. At 50:1 ratio where η ≈ 0.72, this overestimates output torque by 39%. The gearbox frame selected on that overestimate will be undersized for the actual application load.

Quick-Reference Efficiency Values by Ratio (for Torque Calculation)

Use these midpoint efficiency values when calculating output torque. They represent PAO synthetic lubricant at run-in steady-state — the correct reference condition for rated continuous-duty torque calculations:

Service Factor — Why You Must Apply It Before Selecting a Frame

The output torque formula gives you the continuous rated output torque. Before comparing this to the application load, you must calculate the design torque — the service-factor-adjusted value that accounts for duty cycle, shock loading, and daily operating hours:

Source: AGMA 6034-B92 service factor table, adapted for worm gearbox duty classes. For applications with frequent reversals (more than 10 start/stop cycles per hour), add 0.25 to the table value. For applications involving VFD-driven motors with soft-start capability, a 0.25 reduction to the service factor is sometimes permitted — consult the gearbox manufacturer before applying this deduction.

Worked Example 1 — Belt Conveyor Drive (Straightforward)

Application: Horizontal belt conveyor head-pulley drive. Motor: 1.1 kW, 4-pole, 1,400 rpm. Gearbox ratio: 30:1. Operating: 16 hours/day, uniform load. Lubricant: PAO synthetic.

1. Read efficiency from table: Ratio 30:1, PAO run-in → η = 76% (midpoint)
2. Calculate input angular velocity: ω₁ = 1,400 × 2π / 60 = 146.6 rad/s
3. Calculate rated output torque: T₂ = (1,100 W × 0.76 × 30) / 146.6 = 25,080 / 146.6 = 171 Nm
4. Apply service factor: Uniform load, 16 h/day → Sf = 1.25. T₂_design = 171 × 1.25 = 214 Nm
5. Select gearbox: Select NMRV with rated output torque ≥ 214 Nm at 30:1. An NMRV075 at 30:1 is rated ~240 Nm — this is the correct frame. An NMRV063 at 30:1 is rated ~170 Nm — undersized, do not use.

Note: if the calculation had omitted the efficiency factor (T₂ = T₁ × i = 7.51 × 30 = 225 Nm), the pre-service-factor torque appears larger than the correctly calculated 171 Nm. With service factor applied: 225 × 1.25 = 281 Nm — leading to selection of a larger, more expensive NMRV090. Including efficiency gives the correct (smaller) design torque and the correct frame selection. This is why the efficiency factor is not optional.

Worked Example 2 — Gate Opener (Intermittent, Self-Locking Required)

Application: Commercial sliding gate, 800 kg gate mass, 0.15 m/s travel speed, rack-and-pinion mechanism with 0.12 m pitch radius pinion. Motor: 0.37 kW, 1,400 rpm. Required ratio: 60:1. Duty: 20 cycles/day (<2 h total). Self-locking required to hold gate against wind load.

1. Calculate required output torque from application load: Gate force = mass × friction coefficient × g = 800 × 0.08 × 9.81 = 627 N. Output torque = Force × pinion radius = 627 × 0.12 = 75.2 Nm required
2. Apply service factor: Moderate shock (gate motor start against static friction), <2 h/day → Sf = 1.25. T₂_design = 75.2 × 1.25 = 94 Nm
3. Read efficiency from table: Ratio 60:1, PAO run-in → η = 70%. Self-locking confirmed: 60:1 is firmly in the self-locking range.
4. Back-calculate required input power: P₁ = T₂_design × ω₂ / η = 94 × (1400/60 × 2π/60) / 0.70 = 94 × 2.44 / 0.70 = 328 W. A 0.37 kW (370 W) motor has 13% power margin — adequate for this intermittent application.
5. Verify rated output torque of selected gearbox exceeds 94 Nm at 60:1. NMRV050 at 60:1 is rated ~105 Nm — adequate. Confirm self-locking in product data sheet.

For precision gate-drive and servo positioning applications requiring tighter torque tolerances and documented backlash, our precision worm gearbox range provides matched-pair selection with <4 arcmin backlash certification.

Worked Example 3 — Agitator Vertical Shaft (24/7 Continuous Duty)

Application: Vertical shaft chemical agitator, required output torque 320 Nm at 47 rpm output. Motor available: 4-pole 1,400 rpm. Ratio required: 1400/47 = 29.8:1 → specify 30:1. Operating: 24 hours/day, 7 days/week. Moderate viscosity peaks (moderate shock).

1. Apply service factor first: Moderate shock, >16 h/day → Sf = 1.75. T₂_design = 320 × 1.75 = 560 Nm
2. Read efficiency: 30:1 ratio, PAO run-in → η = 76%
3. Calculate required input power: P₁ = T₂_design × ω₂ / η = 560 × (47 × 2π / 60) / 0.76 = 560 × 4.92 / 0.76 = 3,624 W → specify 4 kW motor
4. Select gearbox frame: Catalog rated output torque must exceed 560 Nm at 30:1. An NMRV090 at 30:1 is typically rated ~450 Nm — insufficient. Move to NMRV110 at 30:1, rated ~750 Nm — correct frame.
5. Check thermal rating: 24/7 continuous duty at 4 kW input. Verify NMRV110 thermal input-power rating at 30:1 for continuous duty at 20°C ambient ≥ 4 kW. If not, specify a fan-cooled version or apply a thermal derating factor.

For the full NMRV torque and thermal rating tables across all frame sizes and ratios, see the NMRV worm gearbox series product page. For engineering reference data on industrial worm reducer torque ratings and selection methodology, see the industrial worm reducer engineering reference.

Worm Gearbox Output Torque — Quick Calculator

Use this calculator to compute output torque, input power requirement, and annual energy loss for your application. All efficiency values are loaded from the reference table above (PAO synthetic, run-in):

Note: Design torque shown is the minimum gearbox catalog rating required. Select the next standard frame size above this value from the NMRV catalog. Efficiency values are PAO synthetic, run-in steady-state midpoints — use mineral oil values (5–7% lower) for conservative thermal sizing.

5 Common Torque Calculation Mistakes and How to Avoid Them

1. Omitting the efficiency factor: T₂ = T₁ × i (no η) overestimates output torque by 8–37% depending on ratio. Always include η. At 100:1 ratio, the error reaches 37% — enough to select a gearbox two frame sizes too large or too small.
2. Using peak motor power instead of rated power: Some motor nameplates show a short-term peak power. Always use the rated continuous power for gearbox sizing — the value the motor sustains indefinitely. Using peak power overestimates the continuous output torque and leads to thermal overloading of the gearbox in continuous duty.
3. Forgetting to apply service factor: The catalog torque is the sustained mechanical limit. Real applications impose shock loads, reversals, and extended daily running that reduce effective life unless the service factor is applied. Specifying T₂_design = T₂_load without Sf saves one frame size at purchase and costs a premature failure at 18–30 months.
4. Using nominal ratio without checking the exact catalog ratio: NMRV gearboxes are catalogued at nominal ratios (30:1, 50:1) but the actual ratio is often slightly different (e.g., 29.17:1, 49.50:1 depending on wheel tooth count). For output speed-critical applications (conveyor belt speed, filling machine dosing rate), use the exact ratio from the gear data sheet, not the nominal.
5. Ignoring thermal rating for continuous duty: Calculating T₂ and selecting a frame purely on mechanical torque is only half the check for continuous-duty applications above 4 h/day. Always verify the thermal input-power rating from the catalog separately. The thermal limit is frequently more restrictive than the mechanical limit at ratios above 40:1.

Frequently Asked Questions